标题： 环中自发对称性和反对称性破缺 显示英文标题

标题： Spontaneous symmetry and antisymmetry breaking in a ring with two potential barriers

摘要： 我们提出了一种基本设置，在非线性薛定谔方程框架下实现自发对称性破缺（SSB）和自发反对称性破缺（SASB），分别具有自吸引和排斥的立方项，在一个由δ函数势垒分为两个相互对称的盒子的一维环上，势垒位于相对的点上。 该系统与光学和BEC相关。 线性化系统的谱以解析和数值形式找到。 通过变分近似预测了SSB和SASB，并以数值形式进行了研究。 发现了一个特定的稳定解，表现出强烈的不对称性，以精确形式存在。 在具有吸引力非线性的系统中，对称基态的SSB由调制不稳定性引发。 它通过超临界分岔产生静态不对称状态。 在自排斥系统中，SASB使最低的反对称激发态不稳定，将其转化为反对称性破缺的振荡模式。 显示英文摘要

摘要： We propose a fundamental setup for the realization of spontaneous symmetry breaking (SSB) and spontaneous antisymmetry breaking (SASB) in the framework of the nonlinear Schroedinger equation with the self-attractive and repulsive cubic term, respectively, on a one-dimensional ring split in two mutually symmetric boxes by delta-functional potential barriers, placed at opposite points. The system is relevant to optics and BEC. The spectrum of the linearized system is found in analytical and numerical forms. SSB and SASB are predicted by dint of the variational approximation, and studied in the numerical form. A particular stable solution, which demonstrates strong asymmetry, is found in an exact form. In the system with the attractive nonlinearity, the SSB of the symmetric ground state is initiated by the modulational instability. It creates stationary asymmetric states through a supercritical bifurcation. In the self-repulsive system, SASB makes the lowest antisymmetric excited state unstable, transforming it into an antisymmetry-breaking oscillatory mode.